On a generalized divisor problem II
نویسندگان
چکیده
منابع مشابه
Generalized divisor problem
In 1952 H.E. Richert by means of the theory of Exponents Pairs (developed by J.G. van der Korput and E. Phillips ) improved the above O-term ( see [8] or [4] pag. 221 ). In 1969 E. Krätzel studied the three-dimensional problem. Besides, M.Vogts (1981) and A. Ivić (1981) got some interesting results which generalize the work of P.G. Schmidt of 1968. In 1987 A.Ivić obtained Ω-results for ∫ T 1 ∆ ...
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Let ∆(x) denote the error term in the Dirichlet divisor problem, and E(T ) the error term in the asymptotic formula for the mean square of |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain ∫ T 0 |E(t)| dt ≪ε T 2+ε and ∫ T 0 |E∗(t)| 544 75 dt ≪ε T 601 225 . It is also shown how bounds for moments of |E∗(t)| lead to bounds for moments of |ζ( 1 2 ...
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tact, whereas those for a = 0.02 imply only 25% more frequent contacts than the all-ornone hypothesis but with rather high though rapidly diminishing attack rates. 10 Schuman and Doull, Amer. Jour. Pub. Health, 30, Supplement to March, 1940, p. 21, state: "From these estimates of carrier prevalence and froni the average annual increment in Shick-negatives, an estimate may be made of the number ...
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1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2003
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000008564